We construct a family of right coideal subalgebras of quantum groups, which have the property that all irreducible representations are one-dimensional, and which are maximal with this property. The obvious examples for this are the standard Borel subalgebras expected from Lie theory, but in a quantum group there are many more. Constructing and classifying them is interesting for structural reasons, and because they lead to unfamiliar induced (Verma-)modules for the quantum group. The explicit family we construct in this article consists of quantum Weyl algebras combined with parts of a standard Borel subalgebra, and they have a triangular decomposition. Our main result is proving their Borel subalgebra property. Conversely we prove under some restrictions a classification result, which characterizes our family. Moreover we list for U_q(₄) all possible triangular Borel subalgebras, using our underlying results and additional by-hand arguments. This gives a good working example and puts our results into context.

我们构造了一个量子群的右共代子代数族，它们具有以下性质：所有不可约表示都是一维的，并且具有该性质的最大值。显而易见的例子是李理论所期望的标准Borel子代数，但是在一个量子群中，还有更多的子代数。由于结构上的原因，构造和分类它们很有趣，因为它们会导致量子组的陌生诱导（Verma-）模块。我们在本文中构建的显式族由量子Weyl代数和标准Borel子代数的部分组成，它们具有三角分解。我们的主要结果是证明它们的Borel子代数性质。相反，我们在一定的限制下证明了分类结果，这是我们家庭的特征。此外，我们列出了U _q（₄）使用我们的基础结果和附加的手工论证，所有可能的三角Borel子代数。这提供了一个很好的工作示例，并将我们的结果放到了上下文中。